History of Islamic Mathematics (Numerical System)
History:— The modern numerical system of 1,2,3,4,5,6,7,8, and 9; were a unique set of numbers invented by Spanish Muslims.^{[1]} and were based on the angles they made.^{[2]} The Indian numerical system, it's inspiration, underwent several drastic changes before this new system was created over the course of a few centuries (969—c. 1300s). This was because the Indian numerical system was primitive and problematic to use; requiring the use of physical equipment, not pen and paper, which was a major disadvantage when it came to it's practicality; Hassan alUqlidisi for instance wrote, that the "[o]ficial scribes nevertheless avoid using [the Indian system] because it requires equipment [like a dust board] and they consider that a system that requires nothing but the members of the body [ie their own body parts] is more secure and more fitting to the dignity of a leader.".^{[3]} As a result he invented new methods,^{[n. 1]} as a way to solve for problems using only penandpaperalgorithms he himself developed,^{[4]} and thus became the first person in history to thus do so.^{[n. 2]} The Indian numerical system was mainly used by astrologer mystics, and was similarly like the Chinese system based on 10s.^{[5]} By the 1300's, the Eastern Arabic numerals underwent another revolutionary change in the Western Arabic territories to what they look like today; the Ghubar/Western Arabic numericals.^{[6]} Even according to the "National Institute of Sciences of India" (1962), "The[se] Ghubar numerals resemble modern European numerals much more closely than do the Hindu numerals".^{[7]} Therefore it is incorrect to call modern numerals "Hindu numerals".^{[n. 3]} 

Sources
Footnotes
 ^
 Quote: "However, it was gradually replaced by algorithms performed with pen and paper. The earliest text to describe these new methods was al Uqlidisi's Arithmetic, written in Baghdad in 945 C.E.; in it the author argues for penandpaper techniques so that arithmetics could be distinguished from the dust boardwielding astrologers".
 Thomas F. Glick; Steven Livesey; Faith Wallis (27 January 2014). Medieval Science, Technology, and Medicine: An Encyclopedia. Routledge. p. 46. ISBN 9781135459321.
 ^
In 952, Abu'l Hasan Ahmad ibn Ibrahim alUqlidisi became the first person in the world to solve the Indian numerical system without having to use the dust board as the Indians had been doing for centuries (the Indians had never used penandpaper algorithms to solve their mathematical problems); this is proven by the following peerreviewed sources on the history of the numerals;
 Quote: "A step forward in the development of the decimalplace value system was due to Abu'l Hasan Ahmad ibn Ibrahim alUqlidisi (920980)...who gave algorithms for use with pen and paper [in 1952], as opposed to those of alKhwarizmi which were for dust board, and, more importantly introduced decimal fractions."
 Ethan D. Bloch (14 May 2011). The Real Numbers and Real Analysis. Springer Science & Business Media. p. 54. ISBN 9780387721774.
 The Indian numerical system never used penandpaper style algorithmic arithmetic:
 Historians note that "[f]rom their origins in the late eighth and early ninth centuries, the numerals spread throughout the Islamic world, though not without resistance or confusion. Many conservative scribes and bookkeepers resisted the new numerals in favour of older calculation on the fingers and with numerical words.
 Historians say "[t]he Arabs borrowed not only the Indian numerals, but also a host of computational techniques and devices, including the dustboard, a flat tablet strewn with sand into which figures could be written for undertaking computations...Other techniques available included complex Greekderived system of finger reckoning and the use of shells; accordingly, the use of written penandpaperarithmetic was apparently not part of the initial practice of Indian derived numeration."
 After the work of alUqlidisi, only then did penandpaperarithmetic began to be widely used, the same time; well after his algorithms on penandpaper arithmetic been published and disseminated across the world; "[y]et once the [treatise] had been established by the eleventh and twelfth centuries, Arabic mathematical texts began to advocate doing computations with paper and ink instead of the dustboard".
 Stephen Chrisomalis (2010). Numerical Notation: A Comparative History. Cambridge University Press. p. 215. ISBN 9780521878180.
 ^ This is by the very nature of the numerals. Despite this, the Muslim numerical system is still spuriously referred to as "Indian", when this is far from the case. Indian historians even call the numericals by the separate system themselves; by it's proper name of "Ghubar".
 Bulletin of the National Institute of Sciences of India. National Institute of Sciences of India. 1962. pp. 27–28.
 ^
 Quote: "However, it was gradually replaced by algorithms performed with pen and paper. The earliest text to describe these new methods was al Uqlidisi's Arithmetic, written in Baghdad in 945 C.E.; in it the author argues for penandpaper techniques so that arithmetics could be distinguished from the dust boardwielding astrologers".
 Thomas F. Glick; Steven Livesey; Faith Wallis (27 January 2014). Medieval Science, Technology, and Medicine: An Encyclopedia. Routledge. p. 46. ISBN 9781135459321.
 ^
In 952, Abu'l Hasan Ahmad ibn Ibrahim alUqlidisi became the first person in the world to solve the Indian numerical system without having to use the dust board as the Indians had been doing for centuries (the Indians had never used penandpaper algorithms to solve their mathematical problems); this is proven by the following peerreviewed sources on the history of the numerals;
 Quote: "A step forward in the development of the decimalplace value system was due to Abu'l Hasan Ahmad ibn Ibrahim alUqlidisi (920980)...who gave algorithms for use with pen and paper [in 1952], as opposed to those of alKhwarizmi which were for dust board, and, more importantly introduced decimal fractions."
 Ethan D. Bloch (14 May 2011). The Real Numbers and Real Analysis. Springer Science & Business Media. p. 54. ISBN 9780387721774.
 The Indian numerical system never used penandpaper style algorithmic arithmetic:
 Historians note that "[f]rom their origins in the late eighth and early ninth centuries, the numerals spread throughout the Islamic world, though not without resistance or confusion. Many conservative scribes and bookkeepers resisted the new numerals in favour of older calculation on the fingers and with numerical words.
 Historians say "[t]he Arabs borrowed not only the Indian numerals, but also a host of computational techniques and devices, including the dustboard, a flat tablet strewn with sand into which figures could be written for undertaking computations...Other techniques available included complex Greekderived system of finger reckoning and the use of shells; accordingly, the use of written penandpaperarithmetic was apparently not part of the initial practice of Indian derived numeration."
 After the work of alUqlidisi, only then did penandpaperarithmetic began to be widely used, the same time; well after his algorithms on penandpaper arithmetic been published and disseminated across the world; "[y]et once the [treatise] had been established by the eleventh and twelfth centuries, Arabic mathematical texts began to advocate doing computations with paper and ink instead of the dustboard".
 Stephen Chrisomalis (2010). Numerical Notation: A Comparative History. Cambridge University Press. p. 215. ISBN 9780521878180.
 ^ This is by the very nature of the numerals. Despite this, the Muslim numerical system is still spuriously referred to as "Indian", when this is far from the case. Indian historians even call the numericals by the separate system themselves; by it's proper name of "Ghubar".
 Bulletin of the National Institute of Sciences of India. National Institute of Sciences of India. 1962. pp. 27–28.
References
 ^ ^{a} ^{b} Solomon Gandz (November 1931). "The Origin of the Ghubār Numerals, or the Arabian Abacus and the Articuli". Isis (A Journal of the History of Science Society). Vol. 16. Issue No. 2: 393424.
 ^ ^{a} ^{b} Elizabeth Woodcock; Rabah Saoud (2007). 1001 Inventions: Muslim Heritage in Our World. Abdelrahman Aly Abounegm. p. 64. ISBN 9780955242618.
 ^ ^{a} ^{b} J. J. O'Connor and E. F. Robertson (JOC/EFR January 2001). The Arabic numeral system. St. Andrews University. Retrieved May 3rd, 2016.
 ^ ^{a} ^{b} Thomas F. Glick; Steven Livesey; Faith Wallis (27 January 2014). Medieval Science, Technology, and Medicine: An Encyclopedia. Routledge. p. 46. ISBN 9781135459321.
 ^ ^{a} ^{b} Ethan D. Bloch (14 May 2011). The Real Numbers and Real Analysis. Springer Science & Business Media. p. 54. ISBN 9780387721774.
 ^ ^{a} ^{b} Keith Devlin (1 November 2012). The Man of Numbers: Fibonacci's Arithmetic Revolution. A&C Black. pp. 24. ISBN 9781408822487.
 ^ ^{a} ^{b} Bulletin of the National Institute of Sciences of India. National Institute of Sciences of India. 1962. pp. 27–28.